Question: Solve for $x$ : $x^2 - 15x + 50 = 0$
Solution: The coefficient on the $x$ term is $-15$ and the constant term is $50$ , so we need to find two numbers that add up to $-15$ and multiply to $50$ The two numbers $-10$ and $-5$ satisfy both conditions: $ {-10} + {-5} = {-15} $ $ {-10} \times {-5} = {50} $ $(x {-10}) (x {-5}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -10) (x -5) = 0$ $x - 10 = 0$ or $x - 5 = 0$ Thus, $x = 10$ and $x = 5$ are the solutions.